arXiv subjects

Andrea Secchi

Publications and source records attributed to Andrea Secchi.

At least 19 recordsLinked to original sources

arXiv2025

Spins extracted from fermionic states and their entanglement properties

We investigate the spin states obtained by extracting $n$ electrons from closed-shell fermionic states. A partition of the system is defined through the introduction of the extraction modes. We derive the expression of the $n$-body reduced density matrices, which represent the extracted spin states. We show that these states exhibit different forms of spin entanglement, whose detection is discussed in terms of the spin squeezing inequalities.

quant-ph↗

arXiv2025

Hole-spin qubits in germanium beyond the single-particle regime

The intense simulation efforts on hole-spin qubits in germanium have so far focused primarily on singly occupied quantum dots. Here, we theoretically investigate three-hole qubits in germanium and demonstrate that their performance can rival that of single-hole qubits in both strained and unstrained systems. In particular, we find that -- in the widely used quasi-circular geometry -- a three-hole qubit encoding can yield enhancements of the Rabi frequencies of up to two orders of magnitude and a large advantage also in terms of quality factors.

cond-mat.mes-hall↗

arXiv2024

Genuine multipartite entanglement from many-electron systems

We demonstrate that, contrary to common wisdom, genuine multipartite entanglement (GME) can be abundantly generated from simple non-correlated many-electron states. We show that the extracted GME can be maximized via spin-independent transformations derived from the quantum Fourier transform. We further demonstrate the possibility of maximizing the GME through localized orbitals in a variety of realistic systems and correlated states. Towards the exploitation of potentially useful entanglement, we rationalize system-specific and universal features of the extracted GME.

quant-ph↗

arXiv2023

Envelope-function theory of inhomogeneous strain in semiconductor nanostructures

Strain represents an ubiquitous feature in semiconductor heterostructures, and can be engineered by different means in order to improve the properties of various devices, including advanced MOSFETs and spin-based qubits. However, its treatment within the envelope function framework is well established only for the homogeneous case, thanks to the theory of Bir and Pikus. Here, we generalize such theory to the case of inhomogeneous strain. By fully accounting for the relativistic effects and metric aspects of the problem, we derive a complete envelope-function Hamiltonian, including the terms that depend on first and second spatial derivatives of the strain tensor.

cond-mat.mes-hall↗

arXiv2023

Theory of multi-dimensional quantum capacitance and its application to spin and charge discrimination in quantum-dot arrays

Quantum states of a few-particle system capacitively coupled to a metal gate can be discriminated by measuring the quantum capacitance, which can be identified with the second derivative of the system energy with respect to the gate voltage. This approach is here generalized to the multi-voltage case, through the introduction of the quantum capacitance matrix. The matrix formalism allows us to determine the dependence of the quantum capacitance on the direction of the voltage oscillations in the parameter space, and to identify the optimal combination of gate voltages. As a representative example, this approach is applied to the case of a quantum-dot array, described in terms of a Hubbard model. Here, we first identify the potentially relevant regions in the multi-dimensional voltage space with the boundaries between charge stability regions, determined within a semiclassical approach. Then, we quantitatively characterize such boundaries by means of the quantum capacitance matrix. Altogether, this provides a procedure for optimizing the discrimination between states with different particle numbers and/or total spins.

cond-mat.mes-hall↗

arXiv2023

Quantum estimation and remote charge sensing with a hole-spin qubit in silicon

Hole-spin qubits in semiconductors represent a mature platform for quantum technological applications. Here we consider their use as quantum sensors, and specifically for inferring the presence and estimating the distance from the qubit of a remote charge. Different approaches are considered - based on the use of single or double quantum dots, ground and out-of-equilibrium states, Rabi and Ramsey measurements - and comparatively analyzed by means of the discrimination probability, and of the classical and quantum Fisher information. Detailed quantitative aspects result from the multiband character of the hole states, which we account for by means of the Luttinger-Kohn Hamiltonian. Furthermore, general conclusions can be drawn on the relative efficiency of the above options, and analytical expressions are derived for the Fisher information of a generic qubit within the Rabi and Ramsey schemes.

cond-mat.mes-hall↗

arXiv2021

Inter- and intra-band Coulomb interactions between holes in silicon nanostructures

We present a full derivation of the interaction Hamiltonian for holes in silicon within the six-band envelope-function scheme, which appropriately describes the valence band close to the $\boldsymbolΓ$ point. The full structure of the single-hole eigenstates is taken into account, including the Bloch part. The scattering processes caused by the Coulomb interaction are shown to be both intraband and interband, the latter being mostly short-ranged. In the asymptotic long-range limit, the effective potential tends to the screened Coulomb potential, and becomes purely intraband, as assumed in previous models. We apply our model to compute the excitation spectra of two interacting holes in prototypical silicon quantum dots, taking into account different dielectric environments. It is shown that, in the highly screened regime, short-range interactions (both intra- and inter-band) can be very relevant, while they lose importance when there is no screening other than the one proper of the bulk silicon crystal. In the latter case, we predict the formation of hole Wigner molecules.

cond-mat.mes-hall↗

arXiv2021

Interacting holes in Si and Ge double quantum dots: from a multiband approach to an effective-spin picture

The states of two electrons in tunnel-coupled semiconductor quantum dots can be effectively described in terms of a two-spin Hamiltonian with an isotropic Heisenberg interaction. A similar description needs to be generalized in the case of holes due to their multiband character and spin-orbit coupling, which mixes orbital and spin degrees of freedom, and splits $J=3/2$ and $J = 1/2$ multiplets. Here we investigate two-hole states in prototypical coupled Si and Ge quantum dots via different theoretical approaches. Multiband $\boldsymbol{k}\cdot\boldsymbol{p}$ and Configuration-Interaction calculations are combined with entanglement measures in order to thoroughly characterize the two-hole states in terms of band mixing and justify the introduction of an effective spin representation, which we analytically derive a from generalized Hubbard model. We find that, in the weak interdot regime, the ground state and first excited multiplet of the two-hole system display -- unlike their electronic counterparts -- a high degree of $J$-mixing, even in the limit of purely heavy-hole states. The light-hole component additionally induces $M$-mixing and a weak coupling between spinors characterized by different permutational symmetries.

cond-mat.mes-hall↗

arXiv2020

Phonon-mediated superconductivity in strongly correlated electron systems: a Luttinger-Ward functional approach

We use a Luttinger-Ward functional approach to study the problem of phonon-mediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams for the EEI and the resulting theory is therefore nonperturbative in the strength of the latter. We show that one of the building blocks of the theory is the irreducible six-leg vertex related to EEIs. Diagrammatically, this implies five contributions (one of the Fock and four of the Hartree type) to the electronic self-energy, which, to the best of our knowledge, have never been discussed in the literature. Our approach is applicable to (and in fact designed to tackle superconductivity in) strongly correlated electron systems described by generic lattice models, as long as the glue for electron pairing is provided by phonons.

cond-mat.supr-con↗

arXiv2019

Discrete-time construction of nonequilibrium path integrals on the Kostantinov-Perel' time contour

Rigorous nonequilibrium actions for the many-body problem are usually derived by means of path integrals combined with a discrete temporal mesh on the Schwinger-Keldysh time contour. The latter suffers from a fundamental limitation: the initial state on this contour cannot be arbitrary, but necessarily needs to be described by a non-interacting density matrix, while interactions are switched on adiabatically. The Kostantinov-Perel' contour overcomes these and other limitations, allowing generic initial-state preparations. In this Article, we apply the technique of the discrete temporal mesh to rigorously build the nonequilibrium path integral on the Kostantinov-Perel' time contour.

cond-mat.str-el↗

arXiv2018

Adiabatic perturbation theory of nonequilibrium light-controlled superconductivity

Recent experiments, in which Terahertz (THz) light has been used to induce nonequilibrium superconducting states, have raised a number of intriguing fundamental questions. Theoretically, these experiments are most often described within the Floquet formalism, which suffers a number of well-known limitations (e.g. Floquet heating). Alternative approaches rely on heavy numerical methods. In this Article we develop an analytical theory of nonequilibrium superconductivity that combines path integrals on the Kostantinov-Perel' time contour with adiabatic perturbation theory [G. Rigolin, G. Ortiz, and V.H. Ponce, Phys. Rev. A~{\bf 78}, 052508 (2008)]. We consider a general system of electrons and Raman phonons coupled by the Fröhlich interaction, in the presence of a time-dependent external field which acts on the phonon subsystem. The latter is supposed to model the THz light-induced excitation of nonlinear interactions between infrared and Raman phonons. Assuming that the external field has a slow dependence on time, we derive equations for the dynamical superconducting gap, calculating the leading adiabatic term and the first non-adiabatic correction. Our nonequilibrium formulas can be solved numerically with a minimal increase of computational complexity with respect to that needed to calculate the superconducting gap at equilibrium.

cond-mat.supr-con↗

arXiv2016

Non-equilibrium itinerant-electron magnetism: a time-dependent mean-field theory

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the non-equilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of non-equilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of non-equilibrium single-electron Green functions and self-energies. In the particular case of equilibrium, we recover previously known results.

cond-mat.str-el↗

arXiv2015

Spin and orbital exchange interactions from Dynamical Mean Field Theory

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.

cond-mat.str-el↗

arXiv2015

Magnetic interactions in strongly correlated systems: spin and orbital contributions

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles. This allows to determine the parameters of relativistic and non-relativistic magnetic interactions in the effective spin model in terms of equilibrium Green's functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic fields, spin-orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii-Moriya interactions, as well as additional non-diagonal symmetric terms (which may include dipole-dipole interaction). Our procedure provides the complete exchange tensors in a unified framework, including previously disregarded features such as the vertices of two-particle Green's functions and non-local self-energies. We do not assume any smallness in spin-orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin-orbital contributions to magnetism.

cond-mat.str-el↗

arXiv2013

Inter-valley scattering induced by Coulomb interaction and disorder in carbon-nanotube quantum dots

We develop a theory of inter-valley Coulomb scattering in semiconducting carbon-nanotube quantum dots, taking into account the effects of curvature and chirality. Starting from the effective-mass description of single-particle states, we study the two-electron system by fully including Coulomb interaction, spin-orbit coupling, and short-range disorder. We find that the energy level splittings associated with inter-valley scattering are nearly independent of the chiral angle and, while smaller than those due to spin-orbit interaction, large enough to be measurable.

cond-mat.mes-hall↗

arXiv2012

Non-equilibrium magnetic interactions in strongly correlated systems

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name "twist exchange", which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

cond-mat.str-el↗

arXiv2012

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization

We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub-) Kelvin range.

cond-mat.str-el↗

arXiv2010

Wigner molecules in carbon-nanotube quantum dots

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a `Wigner molecule'. Our exact diagonalisation calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy -indeed some of them have already been observed by Deshpande and Bockrath [Nature Phys. 4, 314 (2008)]. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.

cond-mat.mes-hall↗